An algorithm for fault detection and classification method for wide-area protection in Korean transmission systems is proposed. The modeling of 345-kV and 765-kV Korean power system transmission networks using the Electro Magnetic Transient Program - Restructured Version (EMTP-RV) is presented and the algorithm for fault detection and classification in transmission lines is developed. The proposed algorithm uses the Wavelet Transform (WT) and Singular Value Decomposition (SVD). The Singular value of Approximation coefficient (SA) and part Sum of Detail coefficient (SD) are introduced. The characteristics of the SA and SD at the fault conditions are analyzed and used in the algorithm for fault detection and classification. The validation of the proposed algorithm is verified by various simulation results.